Discussion
What signal-to-noise ratio is needed to put a T1 carrier on a 50 kHz line?
Answer: D
Correct answer: 93 db
Shannon's formula gives the required signal-to-noise ratio from the capacity and bandwidth:
\[ 1.544\times 10^{6} = 50{,}000\log_{2}\!\left(1+\frac{S}{N}\right) \Rightarrow \frac{S}{N} \approx 2^{31} \]
and \( 10\log_{10}(2^{31}) \approx 93\ \text{dB} \) - a ratio no real line could sustain, which is why T1 is not carried this way.
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